few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

Understand solving equations as a process of reasoning and explain the reasoning.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Write and interpret numerical expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand properties of multiplication and the relationship between multiplication and division.

Add and subtract within 20.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Solve systems of equations.

Gain familiarity with factors and multiples.

Understand the connections between proportional relationships, lines, and linear equations.

Use polynomial identities to solve problems.

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Interpret the structure of expressions.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Work with equal groups of objects to gain foundations for multiplication.

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

Rewrite rational expressions.

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

Perform arithmetic operations on polynomials.
problem_activity: Problem 1
What is an equation of the line represented in the graph below?
[IMG]
Problem 2
Four lines were used to define the edges of the trapezoid shown below.
[IMG]
Write an equation for each line described below.
a.   Line that passes through points
$$A$$
and
$$B$$
b.   Line that passes through points
$$B$$
and
$$C$$
c.   Line that passes through points
$$C$$
and
$$D$$
d.   Line that passes through points
$$D$$
and
$$A$$
Problem 3
Optional: Play the memory
Matching Game
with linear equations and graphs. Note that this requires some advance preparation.
Directions for students:
Find a partner and clear off your desks.
Separate the cards into a pile with equations and a pile with graphs.
Turn the equation cards over and organize them into rows/columns on one desk.
Turn the graph cards over and organize them into rows/columns on another desk.
On the first person’s turn, turn over an equation card and a graph card. If the cards match, then the player gets to keep the cards. If they do not match, turn the cards over in the same spot. The turn is over.
NOTE: If the player believes she or he has a match, then the player must prove that there is a match. The other player has the option to disagree and explain why. If the other player is right (and the first player was mistaken), then the other player gets to keep the card and then take a turn.
Repeat step 5 for the second player’s turn.
The game is over when all cards have been matched. The person with the most number of pairs wins the round. Another round may be played.


correct_option_index: 14